What is with the time limit idea? Yea it is slightly lame to hide a cv EVER! But the LAMEST form of cv hide and seek is not keeping it away from the country who took the port. That is a valid effort to keep control of it. When they hide it even when control of the port is not even in jeopardy and refuse to let others put it on the offensive is the highest form of timidity and retardedness.
If you want to resolve this, dont take the cv from them, give the new port owners another cv. One more cv is not going to change the balance of power especially if it's being hidden. And now all the carrier battle guys have an excuse if not a obligation to find and engage then enemy cv.